His motive is himself. As Varys once said, "He would see this country burn if he could be king of the ashes." Varys also said earlier in the conversation, that LF was born with no lands, no wealth and no armies. Now he has all three. He's all about consolidating wealth, lands and power.

While LF marrying Sansa to the Boltons makes us all suspicious of his motives, it was a necessary move. Not only did it get Roose Bolton off his back, but in doing so LF ended the relationship between the Boltons and the Crown. He also received the Crown's backing to make him Warden of the North, once the winner of the battle between Stannis and the Boltons is defeated, and Sansa is returned to King's Landing. We know that last part won't be happening, but by then it won't matter: LF will be the man who took bath the North and united the Vale, the Starks, and the Riverlands. LF will have the full backing of three of the seven kingdoms and will be virtually untouchable by the Crown. One step closer to his dream of ruling all of Westeros.

The wrinkle in LF's plan right now is that Sansa currently despises him, but I think if LF can help give her both Winterfell and her family back all will be forgiven. This is why I don't believe the Blackfish conversation was a trap. It's in LF's best interest to reunite Sansa with family and gather power. He won't be remembered as the man who gave Sansa to the Boltons, he'll be remembered as the man who reunited the Tully and Stark houses to take back the North. Putting Sansa in danger or harming Jon's plans to retake Winterfell gets LF nothing. If the Boltons still rule the North he gains nothing. LF can only move up to the next rung on his ladder of chaos if the Boltons fall.